Question

For a normally distributed distribution of variable x, where the mean is 50, and standard deviation is 2.5, calculate: a) the percentile rank of x=45 b) the z-score of x=52.6 c) the percentile rank of x=58 d) the 29.12th percentile e) the 89.74th percentile f) the z-score of x=45 g) the percentile rank of x=49

Answer 1

Z = (x - μ)/SD, where μ = mean.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the percentile ranks relates to the Z scores.

Answer 2

a. 0.5000 - 0.4772 = 0.0228, 2.28%, 2.28th percentile
b. Ƶ = 1.04 = 0.3508
c. 0.5000 + 0.4993 = 0.9993, 99.93%, 99.93rd percentile
d.
e.
f.
g. 0.5000 – 0.1554 =0.3446, 34.46%, 34.46th percentile